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doi: 10.1038/srep08323.

Self-assembled wiggling nano-structures and the principle of maximum entropy production

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Self-assembled wiggling nano-structures and the principle of maximum entropy production

A Belkin et al. Sci Rep..

Abstract

While behavior of equilibrium systems is well understood, evolution of nonequilibrium ones is much less clear. Yet, many researches have suggested that the principle of the maximum entropy production is of key importance in complex systems away from equilibrium. Here, we present a quantitative study of large ensembles of carbon nanotubes suspended in a non-conducting non-polar fluid subject to a strong electric field. Being driven out of equilibrium, the suspension spontaneously organizes into an electrically conducting state under a wide range of parameters. Such self-assembly allows the Joule heating and, therefore, the entropy production in the fluid, to be maximized. Curiously, we find that emerging self-assembled structures can start to wiggle. The wiggling takes place only until the entropy production in the suspension reaches its maximum, at which time the wiggling stops and the structure becomes quasi-stable. Thus, we provide strong evidence that maximum entropy production principle plays an essential role in the evolution of self-organizing systems far from equilibrium.

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Figures

Figure 1
Figure 1. Consecutive snapshots of the sample illustrating the formation of nanotube chains.
The distance between electrodes is 1 cm, applied voltage is400 V, and the series resistor is100 MOhm. Panel (a) demonstrates the photograph of the ER fluid before the voltage is applied and the schematic of the experimental setup. The following photographs are taken after (b)t =45 s, (c)t =90 s and (d)t =1500 s of interaction with E-field.
Figure 2
Figure 2. Normalized power dissipation in the fluid as a function of time,t.
Concentration of nanotubes is0.075 g/l. (a) Complete evolution: curve S1 (black),Rs =10 MΩ,U =75 V; curve S2,Rs =10 MΩ,U =325 V (blue). The timet0 is the time when the maximum possible dissipated power is achieved. (b) Incomplete evolution: curve U1,Rs =100 MΩ,U =5 V; curve U2,Rs =2 MΩ,U =300 V.
Figure 3
Figure 3. The resistance of nanotube chains formed in the fluid at different series resistances.
For eachRs four values ofRf are shown, measured at different timest. Blue diamonds represent the longest evolution time. Applied voltage is150 V, concentration of nanotubes is0.075 g/l. The blue dashed line corresponds toRf =Rs,t0 is the time whenP(t0)/Pmax =1.
Figure 4
Figure 4. Probability density function of the normalized power dissipated in the fluid.
These curves are calculated using the measurements of the type shown in Fig. 2. The probability distributions are calculated for the following time intervals: 0<t <0.1t0, 0 <t <0.5t0, 0 <t <1.0t0 and 0 <t <2.0t0. The total ensemble consists of438820 measured points, corresponding toten independent evolution curves, in whichRs andU had different values.
Figure 5
Figure 5. Motion of the CNT “bug” under the influence of dc electric field.
Panel (a) illustrates positions of the “arms” of the bug when they are retracted (t =T), approaching (t =T+2 s), touching (t =T+3 s) and again retracted (t =T+9 s) from the right electrode. HereT~2500 s. The movie showing the motion of the selfassembled wiggling structure is contained in Supplementary Information online. Panel (b) demonstrates the time dependence of the normalized power dissipated by the bug. Inset: a segment of the time dependence of the normalized power, corresponding to the phase when the bug is fully developed and exhibits the arm motion. Att~4500 s the stable phase begins.
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References

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